Question

Question #28c03

Answer 1

`(kpi)/2, kpi`

Explanation:

5sin 4x + 10sin 2x = 0
Reminder: sin 4x = 2sin 2x.cos 2x:
10sin 2x.cos 2x + 10sin 2x = 0
10sin 2x(cos 2x + 1) = 0
Either sin 2x or (cos 2x + 1) should be zero:
a. sin 2x = 0 -->
`2x = 0 + 2kpi` --> `x = kpi`
`2x = pi + 2kpi` --> `x = pi/2 + kpi`
`2x = 2pi + 2kpi` --> `x = pi + kpi`
b. cos 2x + 1 = 0 --> cos 2x = -1
`2x = + pi + 2kpi`
`x = + pi/2 + kpi`
Answers for [0, 2pi]:
`0, pi/2, pi`
General answers:
`x = (kpi)/2`
`x = kpi`